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Actually it comes from Euler's Laws of Motion applied to a point mass instead of a rigid body (or as they are commonly known as Newton's laws).

Force equals mass times acceleration of the center of gravity. In a pendulum with steady motion, as it is rotating about the $+y$ with speed $\omega$, the tangential speed of the particle is $v=\omega\,r$. The acceleration of the particle, is that of circular motion with radius $r$ or $a = \omega^2 r = v^2/r$.

Since the forces in the vertical direction are balanced then $T\cos\theta = m g$ } $ T = \frac{m g}{\cos\theta}$